SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity

Details SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity

1997-05-28

arxiv.org/abs/gr-qc/9705080v1

Class.Quant.Grav. 15 (1998) 573-580

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages

Scientific paper

10.1088/0264-9381/15/3/009

We consider a space-time with spatial sections isomorphic to the group manifold of SU(2). Triad and connection fluctuations are assumed to be SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform non-perturbative path integral quantization of the model. Contarary to previous claims the path integral measure appeared to be non-singular near configurations admitting additional Killing vectors. In this model we are able to calculate the generating functional of Green functions of the reduced phase space variables exactly.

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